Do you have Comcast cable? If not, which one?
Did you receive a letter from your cableco saying they were going to an "all-digital" system and they're scrambling ALL their channels, so you'd need the adapter to tune any channels at all? This would have been a fairly recent event.
The digital tuner in generic recorders like the Magnavox is not an exact match for any particular cable system: it sorta works but not with all channels on all systems. When your cableco periodically changes around its channel numbers, you'll need to rescan the channels, which some people find very tedious and confusing. At minimum, you should be able to tune your local broadcast channels and some of the "free" (not scrambled) basic cable channels. But again, if you expect the Magnavox to function like your VCR did prior to the digital cable change, you will be disappointed. Since the digital shift, Murphy's Law Of Nasty Cable Tricks means at least one of your favorite channels will require a box to decode it.
In the short term, you'll either get real lucky and the Magnavox will tune all your favorite channels, or you'll endure what most people deal with: some channels need the box while others can still be tuned by the Magnavox (for how much longer, nobody knows). Wiring the Magnavox, your decoder, and your TV to get as many options out of this as possible is a bit tricky: see the instructions in wajo's huge Magnavox thread here on AVS.
Fortunately the Magnavox is sold primarily thru the WalMart website, and is backed by a 30 day refund policy if you don't like the way it works. So it isn't much of a hassle to simply buy one and try it out with your cable system for a couple weeks. There's no other reliable way to determine if it will tune the channels you want: compatibility varies from household to household.
Since they didn't say anything about their system going "all-digital," I'd suggest you get a Mag unit, connect directly to the cable coax (with their adapter removed), do a channel scan ... "Auto Channel Preset > Cable (Analog/DIgital)"... in the Mag, and see what it tunes.
Click the 1st link in my sig. for a list of info and help files, esp. 3.d on Tuning Channels so you know what to expect.
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Edit: How old is your TV. The Mag needs at least a Composite YWR RCA connection on the TV since it only passes thru the raw cable signal thru the coax, unlike your VCR. If your TV is so old it only has a coax connection, you'll have to use your VCR as a "modulator" for the coax input on the TV, or get a separate RF modulator.
Cablevision is up there, too. I think they were the first to get the FCC waiver and scramble everything.
TWC still has an analog band (I've been monitoring it with an analog TV in my bedroom.) They recently dropped a few more channels, but most of the biggies are there (networks, TNT, the cable news channels, etc.)
It would help to know which cable company we're talking about.
They sell a "TiVo"? Is it an actual TiVo-brand DVR? Usually cable companies lease a box with no initial fee, just a monthly fee.